Disk Formation and Jet Driving in Collapsing Cloud Cores Masahiro Machida (Kyushu University)
Star Formation Process Observations have shown that Low-velocity outflows and high-velocity jets are ubiquitous Circumstellar disk formation in the Class 0 stage (Tobin et al. 2012,2015, Murillo et al. 2013, Codella et al.. 2014, Lee et al. 2014, Yen et al. 2015) Planet formation in the early stage (?) Molecular Cloud Core To understand star and disk formation process, we need to clarify Driving mechanism of low-velocity outflows and high-velocity jets Circumstellar disk and planet formation process in collapsing cloud core Protostar, Circumstellar, Disk, Jets
Star forms in Gravitationally Collapsing Cloud Is star formation simple? Spherical symmetry? Magnetic field and rotation cause complexities Both are an anisotropic force Anisotropic structure formation (disk, jet and outflow) Both are conserved Magnetic flux and angular momentum problem Girart+ 09 Arquilla&Goldsmith 86 Disk formation, outflow and jet driving are closely related to B and W We need to understand the star formation process with B and W
Star Formation Process can be Divided into Two Stages Molecular Cloud Core Gas collapsing stage (before p.s. formation) Protostar Formation Gas accretion stage (after p.s. formation) Protostar
Temperature T (K) Pathway for Protostar Formation: Gas Collapsing Phase Larson(1969), Winkler & Newman (1980), Tscharnuter(1987), Masunaga & Inutsuka(2000), Whitehouse & Bate(2006), Stematellos et al.(2007), Bate (2010), Tomida et al.(2010) 10 4 Schematic View of the Protostar Formation Protostar Formation Thermal evolution in the collapsing gas until the protostar formation Epoch Protostar formation 10 3 Molecular cloud Dissociation of H 2 10 2 10 Protostar (Second core) (~0.01AU) Tomida et al. (2013) Gas temperature First adiabatic core formation Masunaga First & Inutsuka Core (2000) (~1-100AU) n (cm -3 ) 10 5 Density 10 10 10 15 10 20 10 4 100 1 0.1 Two Nested Cores Spatial Scale (AU)
This Talk 1. Gas Collapsing Phase before the Protostar Formation 2. Early Gas Accretion Phase ~500 years after the Protostar Formation 3. Long-term Evolution of Circumstellar Disk with Sink
1. Gas Collapsing Phase before the Protostar Formation
Gas Collapsing phase: 2D w/ B w/o non-ideal effects radiation He could reproduced Low-velocity outflow driven by the first core Tomisaka (1998, 2000, 2002)
Gas Collapsing phase: 3D w/ B w/o non-ideal effects w/ radiation Bate (1998, 2010, 2011) First core is the origin of the rotation supported disk!! With rotation, the first core remains after the protostar formation Abstract (the remnant of) the first core is supported by the rotation and becomes to circumstellar disk
Gas Collapsing phase: 3D w/ B w/o non-ideal effects w/o radiation n [cm -3 ] 1 AU Without rotation, first core disappears in ~1 yr after the protostar formation Gas behaves adiabatically at n 10 11 cm -3 Adiabatic (or first core) formation Dissociation of H 2 at n 10 16 cm -3 Rapid collapse again (second collapse) Protostar formation Collapse of the first core remnant Disappearance of F.C Machida & Matsumoto 11
Gas Collapsing phase: 3D w/ B w/o non-ideal effects w/o radiation With rotation, the first core evolves into the rotation supported disk n [cm -3 ] Machida & Matsumoto 11 Protostar First core remnant Rotation supported disk
Gas Collapsing phase: 3D w/ B w/ non-ideal effects w/ radiation Both non-ideal effect of B and radiation are considered Jet Just after p.s. formation, we can see the first core (remnant) or nascent disk in density, temperature, and velocity profiles Density Protostar Rotation supported disk Color: density Temperature Velocity Tomida et al. (2013) The protostar formation process was successfully simulated Protostar, nascent disk, low-velocity outflow, high-velocity jet were well reproduced But, only 1 years after protostar formation
Recent Study of Gas Collapsing phase Induction equation Ohmic Hall Ambipolar w/ non-ideal effects w/ radiation Both radiation non-ideal MHD effect of Ohmic, ambipolar and Hall terms are considered Tomida et al. (2015): Ohmic + ambipolar diffusion, just before the protostar formation epoch, Nested Grid Tsukamoto et al. (2015): Ohmic + ambipolar diffusion until the protostar formation, SPH Tsukamoto et al. in preparation: Ohmic + ambipolar diffusion + Hall term
Tomida + 15 Basic Equations (w/o div B cleaning) Mass Conservation Eq. of motion Induction eq. Gas Energy Eq. div B=0 Poisson s Eq. Radiation Transfer + Eq. of state + AD & OD rates + Opacities
Tomida + 15 Non-ideal MHD Models: First Cores OD Only OD+AD 18AU 18AU OD: Slow-rotating, vertical inflation by heating from second core AD: Supported by rotation, non-axisymmetric (GI), but size is still small
Tomida + 15 Outflows by radiation+shock heating -> magnetic pressure driven jets Disk Formation after 2nd Collapse OD Only, ρ OD Only, Tg 2AU A rotationally-supported disk is formed after protostellar core formation.
Tomida + 15 Force Balance Ideal MHD OD Only OD+AD Ideal MHD model is essentially not rotating, and is totally supported by the gas pressure. OD model has considerable rotation, but not enough to support the first core and it is still pressure supported. Rotation is dominant, but not by far, in OD+AD model. The gas pressure is still contributing.
SPH: Non-Ideal (Ohmic + Ambipolar diff.) Radiation MHD Tsukamoto+ 15 Rotation supported disk forms at the same epoch of the protostar formation with B diffusion Angular Momentum J Ohm + Ambipolar Density Temperature Plasma b Ideal Ideal MHD Density + Ohmic Disk is massive and gravitationally unstable G.I. is expected to play an important role in a further evolutionary stage + Ohmic + Ambipolar
2. Early Gas Accretion Phase ~500 years after the Protostar Formation
Magnetic Field Gas Accretion phase: 3D w/ B w/o non-ideal effect w/o radiation Ω 0 Resistive MHD eqs. Initial Condition Ω Rotation Axis (, T) P P( ), (Barotropic eos + Protostellar Model) Bonnor-Ebert Sphere 4.6x10 4 AU Molecular Cloud core In this study, Both protostar (h<0.01au) and molecular cloud core >10 5 AU are spatially resolved Cloud evolution was calculated for >500 years after the protostar formation Without Sink With huge computational time (~10 months (wall clock time))
Gravitational Instability & Magnetic Effects Plasma b b>10 3 (very weak B) Jet b<10 (Strong B) high b region Keplerian Disk Equatorial plane Non-axisymetric strcuture due to G.I. color:plasma b contour: density (left) b (right) Magnetic field dissipates in a high density gas region y=0 plane >~3 AU (magnetic coupling region): magnetic braking, low-velocity outflow low b Protostar region ~0.5 < r < 3 AU (magnetic decoupling region): non-axisymmetric structure by G.I <~0.5 AU (magnetic coupling region): (tower) jet, magnetic braking, MRI (disk surface)
Time variability of Outflow and Jet Episodic Jets cause Episodic Accretion (a) Mass (b) Momentum (c) Kinetic energy (d) Outflow and inflow rates
Jets, Outflow, Disk and Protostar High-velocity jet is driven near the protostar Schematic view Low-velocity outflow is driven by the outer disk region High-velocity jet is enclosed by the low-velocity outflow Large scale Simulation Small scale
Sink? We cannot calculate this phase for a long time without cheating (sink) Molecular Cloud Gas Collapsing Stage Gas Accretion Stage F.C. formation P.S. formation Disk formation? To calculate the disk formation process Class 0 Class I Class II serious calculation without sink an impracticably huge CPU time (power) is required easy calculation with sink we can easily acquire outcomes! (However, we donot know whether the outcomes are correct or not) Sink method (there are many prescriptions) A high-density gas region requires a short time step which impedes a long time disk evolution a high density region is masked and is removed an inner boundary is imposed around the protostar
Serious Caution? Machida, Inutsuka, Matsumoto (2014) Starting from the same initial condition, the disk formation was calculated with different sink sizes Results dramatically and qualitatively differ with different sink treatment (or sink radius) Sink radius of <1AU and spatial resolution of <0.1 AU are inevitably needed r acc =6.7 AU large sink No disk forms Uniform Sphere Same settings as in Seifried et al. r acc = 12.6AU completely different outcome! n trh =3x10 11 cm -3 No disk forms r acc = 1AU small sink Disk forms! r acc = 1 AU n trh = 10 13 cm -3 Large disk appears!
Long-term evolution of disk with r sink < 1 AU Even with strong magnetic field, the rotation supported disk forms in very early phase of star formation (Class 0 phase) ratio of v f to Keplerian vel. Machida, Inutsuka, Matsumoto (2014) See also Dapp & Basu 10, 12
Exponential Disk Growth The disk rapidly grows as the infalling envelope dissipates. disk radius Disk-to-envelope mass ratio Slowly rotating massive infalling envelope magnetic field lines rapidly rotating less massive disk
Evolution of Outflow As the disk grows, the outflow also grows As the infalling envelopes dissipates, the outflow weakens and finally disappears Star forming cloud (Molecular cloud core)
Gravitational Instability and Planet Formation Disk gravitational instability without sink Fragmentation occurs in the disk But, fragments falls onto the protostar Gravitational instability inevitably occurs during the early phase of star formation Machida & Nakamura 15 Inutsuka et al. 2010 See also Vorobyov, Basu et al.
Summary The star formation process from prestellar cloud until protostar and circumstellar disk formation have been investigated using numerical simulations Recent theoretical studies indicates that The first core forms before the protostar formation and evolves into the protostar formation: the first core is the origin of circumstellar disk The low-velocity outflow is driven by the first core or outer disk region, while jets are driven near the protostar: the magnetic dissipation region causes two distinct flows The dissipation of magnetic field occurs in the first core or nascent disk and alleviates the angular momentum transfer due to magnetic braking To accurately investigate the disk formation, sink radius of < 1AU and spatial resolution of ~0.1AU are inevitably needed The size of rotation disk is within ~10 AU during the Class 0 stage, while the disk size exponentially grows as the infalling envelope dissipates and reaches ~100 AU Gravitational instability occurs and tends to form planetary mass objects during the (early) gas accretion phase